Modeling and Analysis of Daily Rainfall Data

Abstract

In this work we have tried to develop a statistical model for the daily rainfall measurements. Data series from Bergen the last 107 years and from Sviland, Rogaland, the last 115 years, obtained by The Norwegian Meteorological Institute, has specifically been studied. This statistical approach is based only on measured precipitation data. The high frequency of daily data may contain important information of the underlying meteorological process and we investigate possibilities to extract this information. Simple parametric modeling with components for seasonal variation is used to represent the data. A parsimonious parametric model may contribute to increased statistical power of analyses and hypothesis testing of possible changes in the meteorological process. Our parametric model with quite few parameters can used for a detailed study of the properties of trends and changes over time. Properties such as occurrence of wet days, expected amount of rain, spell lengths and extreme events are of special interest. Similar modeling of daily rainfall data has been used by others, but not for the same purposes as we suggest. We have used generalized linear models as statistical tool for fitting the data to the model. Based on simulation studies, comparisons of model estimated quantities and corresponding data quantities, the model seems to fit series of daily rainfall data very well. We also combine this modeling with techniques for statistical process control to detect changes in the rainfall process. For two particular series considered, we see indications of development in jumps between levels rather than slowly evolving trends.